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On Relaxation Oscillations Governed by a Second Order Differential Equation for a Large Parameter and with a Piecewise Linear Function(1)

Published online by Cambridge University Press:  20 November 2018

K. K. Anand
K. K. Anand*
Affiliation:
Department of Mathematics, Concordia UniversitySir George Williams Campus, Montreal, P.Q.
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Abstract

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This paper deals with the differential equation: ẍ + μF(ẋ) + x = ƒ( X, ẋ, t/Tμ) for μ ≫ 1 where F is a piecewise linear function and f is a periodic function of period μT, where T is to be chosen. It is established that periodic forced vibrations exist in an annular domain R(μ) constructed for the free vibration (ƒ ≡ 0), provided ƒ is not of higher order than Subsequently with ƒ = A cos (2πt/μT*), an asymptotic treatment of the forced vibration problem is carried out, by finding the proper initial conditions and the proper period μT* of f. Finally it is concluded that μT* is close to the period of the free vibration.

Keywords

34-0234C254E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 1 , 01 March 1983 , pp. 80 - 91
Copyright
Copyright © Canadian Mathematical Society 1983

Footnotes

(l)

This paper has been extracted from a thesis with the same title submitted and approved at Courant Institute of Mathematical Sciences, New York University, New York in 1980.

References

1. Anand, K. K., On Relaxation Oscillations Governed by a Second Order Differential Equation for a Large Parameter and with a Piecewise Linear Function, Thesis approved in 1980 by Courant Institute of Mathematical Sciences N.Y.U., available with Microfilms International or Courant Institute Library.Google Scholar
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3. Grasman, J., Veling, E. J. M. and Willems, G. M.; Relaxation Oscillations Governed by a van der Pol equation with periodic forcing term; Mathematisch Centrum Amsterdam 1975.Google Scholar
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